hey welcome to the forum!
as far as I know, I haven't seen or know of any companies that make super customized go karts that aren't sold as complete kits for retail. most of the ones I've seen on youtube are project go karts that are chopped up, renforced frames, fabricated motor mounts, with some other engine from a streetbike, dirtbike, snowmobile, or car... etc... you can try contacting them to see if they can build you one but I know its going to cost some serious money if they do!
not sure on how much you are willing to spend but racing go karts like shifter and non-shifters alone start from $2500 to $5500 and up. I'd expect seeing some crazy price to have one custom build, just for the labor, time, and materials.
your best bet is to find a used frame (ex. craigslist or ebay) get an engine that suits you and will be happy with, get some racing go kart wheels, also the rest of the steering assembly and everything else like bearings, axle, and brakes... etc... draw out the plans and build it yourself (if you have the tools and know hows) or pay someone to weld or put it together for you?
others on this forum may have better tips but here are some links that use for my personal racing gokart and homemade "might help you in the right direction" the rest is up to you to do some research
http://www.rc-trucks.org/go-cart-kits.htm
http://www.pslkarting.com/shop/index.php?cPath=49
http://www.trackmagic.com/
http://www.fastech-racing.com/
(not sure if its ok to paste links on the forum but if its a no no, please remove my post on this thread)